Pre Calculus Evaluating HELP?

Question

Please show all the work out (if possible) 
Thank you!

Answer 1

The functions are  f(x) = x² , g(x) = 2x + 5 and h(x) = x² - 1

1) f[g(x - 1)]

g(x) = 2x + 5

g(x - 1) = 2(x - 1) + 5 = 2x - 2 + 5 = 2x  + 3

f[g(x - 1)] = f(2x + 3)

               = (2x + 3)²

              = 4x² + 9 + 12x

f[g(x - 1)] = 4x² + 9 + 12x

2) g[h(x³ )]

h(x) = x² - 1

h(x³ ) = (x³ )² - 1 = x⁶ - 1

g[h(x³ )] = g(x⁶ - 1)

             = 2(x⁶ - 1) + 5

            = 2x⁶ - 2 + 5

            = 2x⁶ + 3

g[h(x³ )] = 2x⁶ + 3

3) g(f(a + h))

f(x) = x²

f(a + h) = (a + h)²

g(f(a + h)) = g((a + h)² )

                = 2[(a + h)²]+ 5

                = 2[a² + h² + 2ah] + 5

               = 2a² + 2h² + 4ah + 5

g(f(a + h)) = 2a² + 2h² + 4ah + 5